Compression of Weighted Graphs

We propose to compress weighted graphs (networks), motivated by the observation that large networks of social, biological, or other relations can be complex to handle and visualize. In the process also known as graph simplication, nodes and (unweighted) edges are grouped to supernodes and superedges, respectively, to obtain a smaller graph. We propose models and algorithms for weighted graphs. The interpretation (i.e. decompression) of a compressed, weighted graph is that a pair of original nodes is connected by an edge if their supernodes are connected by one, and that the weight of an edge is approximated to be the weight of the superedge. The compression problem now consists of choosing supernodes, superedges, and superedge weights so that the approximation error is minimized while the amount of compression is maximized. In this paper, we formulate this task as the 'simple weighted graph compression problem'. We then propose a much wider class of tasks under the name of 'generalized weighted graph compression problem'. The generalized task extends the optimization to preserve longer-range connectivities between nodes, not just individual edge weights. We study the properties of these problems and propose a range of algorithms to solve them, with dierent balances between complexity and quality of the result. We evaluate the problems and algorithms experimentally on real networks. The results indicate that weighted graphs can be compressed efficiently with relatively little compression error.

A fault-tolerant multi-transputer architecture

A new fault-tolerant multi-transputer architecture capable of tolerating failure of any one component in the system is described. In the proposed architecture the processing nodes are automatically reconfigured in the event of a fault and the computations continue from the stage where the fault occurred. The process of reconfiguration is transparent to the user, and the identity of the failed component is communicated to the user along with the results of computations. Parallel solution of a typical engineering problem involving solution of Laplace's equation by the boundary element method has been implemented. The performance of the architecture in the event of faults has been investigated.

Jakojuuriviljelyn vaikutus kasvihuonekurkun (Cucumis sativus L.) kasvuun ja kehitykseen

Kasvit ottavat vettä parhaiten kasteluravinneliuoksesta, jonka ravinnepitoisuus on pieni. Intensiivisessä kasvihuonetuotannossa käytetään silti kastelulannoituksessa usein korkeita ravinnepitoisuuksia ravinnepuutosten ja satotappioiden välttämiseksi. Jakojuuriviljelyssä kasvin juuriston annetaan kasvaa kahteen erilliseen kasvualustaosioon. Tällöin toiselle puolelle annetaan johtokyvyltään väkevää ja toiselle puolelle laimeaa ravinneliuosta. Erityisesti kasvihuonekurkun, joka on herkkä kasvualustan suolaisuuden aiheuttamille vedensaantiongelmille, on todettu hyötyvän tästä tekniikasta, mikä näkyy kasvaneina satoina. Tämän MTT Piikkiössä toteutetun kasvihuonekurkun jakojuuriviljelytutkimuksen tavoitteena oli tarkentaa tekniikkaa erityisesti kasteluliuosten johtokyvyn osalta. Yhtenäisjuuriviljelyn ja perinteisen jakojuuriviljelyn lisäksi kokeessa oli kaksi jakojuuriviljelykäsittelyä, joissa ravinneliuosväkevyyksiä vaihdettiin väliajoin juuriston toimintakyvyn parantamiseksi. Erillisessä osakokeessa tutkittiin erilaisten johtokyky-yhdistelmien vaikutusta kasvihuonekurkun vegetatiiviseen kasvuun maanpäällisten ja -alaisten kasvinosien välillä sekä juurten morfologiaan ja anatomiaan. Tulokset osoittivat, että jakojuuriviljely lisäsi kasvihuonekurkun sadontuottoa jopa 16 %, mutta ei vaikuttanut koko viljelykauden veden tai ravinteiden ottoon. Yhtenäisjuuriviljelyssä muodostui eniten piikkikärkisiä hedelmiä, mikä viittaa vedensaantiongelmiin haihdutustarpeen ollessa suurin. Viljelytekniikalla ei ollut vaikutusta kasvien vegetatiiviseen kasvuun tai kasvuston rakenteeseen. Lehtiruodeista tehdyt nitraatti- ja kaliummittaukset osoittivat, ettei kasteluliuosten ravinnepitoisuuksilla ollut vaikutusta juurten ravinteiden ottoon. Erilaisilla johtokyky-yhdistelmillä oli huomattavampi vaikutus kasvihuonekurkun juurten painoon kuin verson painoon tai varren pituuskasvuun. Lehtiruotianalyysit viittasivat ravinteiden erilaiseen allokointiin eri johtokyky-yhdistelmissä. Korkeiden johtokykyjen aiheuttama osmoottinen stressi johti muutoksiin juurten morfologiassa ja anatomiassa. Tulosten perusteella jakojuuriviljely paransi kehittyvien hedelmien kohdevahvuutta suhteessa muihin kohteisiin vaikuttamatta vegetatiiviseen kasvuun. Kun laimean ja väkevän ravinneliuoksen puolia vaihdettiin, juuristo otti joustavasti vettä ja ravinteita olosuhteiden määräämästä edullisemmasta johtokyvystä, jolloin kasvihuonekurkun viljelyssä saavutettiin merkittävä satoetu. Juuriston jakaminen vaikuttanee kasvien hormoniaineenvaihduntaan ja voi heikentää juuriston kasvua heikentämättä sen toimintakykyä, jolloin yhteyttämistuotteita kohdennetaan tehokkaammin maanpäällisten osien kasvuun.

Algorithms for Exact Structure Discovery in Bayesian Networks

Bayesian networks are compact, flexible, and interpretable representations of a joint distribution. When the network structure is unknown but there are observational data at hand, one can try to learn the network structure. This is called structure discovery. This thesis contributes to two areas of structure discovery in Bayesian networks: space--time tradeoffs and learning ancestor relations. The fastest exact algorithms for structure discovery in Bayesian networks are based on dynamic programming and use excessive amounts of space. Motivated by the space usage, several schemes for trading space against time are presented. These schemes are presented in a general setting for a class of computational problems called permutation problems; structure discovery in Bayesian networks is seen as a challenging variant of the permutation problems. The main contribution in the area of the space--time tradeoffs is the partial order approach, in which the standard dynamic programming algorithm is extended to run over partial orders. In particular, a certain family of partial orders called parallel bucket orders is considered. A partial order scheme that provably yields an optimal space--time tradeoff within parallel bucket orders is presented. Also practical issues concerning parallel bucket orders are discussed. Learning ancestor relations, that is, directed paths between nodes, is motivated by the need for robust summaries of the network structures when there are unobserved nodes at work. Ancestor relations are nonmodular features and hence learning them is more difficult than modular features. A dynamic programming algorithm is presented for computing posterior probabilities of ancestor relations exactly. Empirical tests suggest that ancestor relations can be learned from observational data almost as accurately as arcs even in the presence of unobserved nodes.

Distributed Coding for Multiple Access Communication with Side Information

In a typical sensor network scenario a goal is to monitor a spatio-temporal process through a number of inexpensive sensing nodes, the key parameter being the fidelity at which the process has to be estimated at distant locations. We study such a scenario in which multiple encoders transmit their correlated data at finite rates to a distant, common decoder over a discrete time multiple access channel under various side information assumptions. In particular, we derive an achievable rate region for this communication problem.

A non-cooperative game-theoretic approach to channel assignment in multi-channel multi-radio wireless networks

Channel assignment in multi-channel multi-radio wireless networks poses a significant challenge due to scarcity of number of channels available in the wireless spectrum. Further, additional care has to be taken to consider the interference characteristics of the nodes in the network especially when nodes are in different collision domains. This work views the problem of channel assignment in multi-channel multi-radio networks with multiple collision domains as a non-cooperative game where the objective of the players is to maximize their individual utility by minimizing its interference. Necessary and sufficient conditions are derived for the channel assignment to be a Nash Equilibrium (NE) and efficiency of the NE is analyzed by deriving the lower bound of the price of anarchy of this game. A new fairness measure in multiple collision domain context is proposed and necessary and sufficient conditions for NE outcomes to be fair are derived. The equilibrium conditions are then applied to solve the channel assignment problem by proposing three algorithms, based on perfect/imperfect information, which rely on explicit communication between the players for arriving at an NE. A no-regret learning algorithm known as Freund and Schapire Informed algorithm, which has an additional advantage of low overhead in terms of information exchange, is proposed and its convergence to the stabilizing outcomes is studied. New performance metrics are proposed and extensive simulations are done using Matlab to obtain a thorough understanding of the performance of these algorithms on various topologies with respect to these metrics. It was observed that the algorithms proposed were able to achieve good convergence to NE resulting in efficient channel assignment strategies.

A Cache coherence protocol for MIN-based multiprocessors

In this paper we present a cache coherence protocol for multistage interconnection network (MIN)-based multiprocessors with two distinct private caches: private-blocks caches (PCache) containing blocks private to a process and shared-blocks caches (SCache) containing data accessible by all processes. The architecture is extended by a coherence control bus connecting all shared-block cache controllers. Timing problems due to variable transit delays through the MIN are dealt with by introducing Transient states in the proposed cache coherence protocol. The impact of the coherence protocol on system performance is evaluated through a performance study of three phases. Assuming homogeneity of all nodes, a single-node queuing model (phase 3) is developed to analyze system performance. This model is solved for processor and coherence bus utilizations using the mean value analysis (MVA) technique with shared-blocks steady state probabilities (phase 1) and communication delays (phase 2) as input parameters. The performance of our system is compared to that of a system with an equivalent-sized unified cache and with a multiprocessor implementing a directory-based coherence protocol. System performance measures are verified through simulation.

Explicit and Optimal Exact-Regenerating Codes for the Minimum-Bandwidth Point in Distributed Storage

In the distributed storage setting that we consider, data is stored across n nodes in the network such that the data can be recovered by connecting to any subset of k nodes. Additionally, one can repair a failed node by connecting to any d nodes while downloading beta units of data from each. Dimakis et al. show that the repair bandwidth d beta can be considerably reduced if each node stores slightly more than the minimum required and characterize the tradeoff between the amount of storage per node and the repair bandwidth. In the exact regeneration variation, unlike the functional regeneration, the replacement for a failed node is required to store data identical to that in the failed node. This greatly reduces the complexity of system maintenance. The main result of this paper is an explicit construction of codes for all values of the system parameters at one of the two most important and extreme points of the tradeoff - the Minimum Bandwidth Regenerating point, which performs optimal exact regeneration of any failed node. A second result is a non-existence proof showing that with one possible exception, no other point on the tradeoff can be achieved for exact regeneration.

A Flexible Class of Regenerating Codes for Distributed Storage

In the distributed storage setting introduced by Dimakis et al., B units of data are stored across n nodes in the network in such a way that the data can be recovered by connecting to any k nodes. Additionally one can repair a failed node by connecting to any d nodes while downloading at most beta units of data from each node. In this paper, we introduce a flexible framework in which the data can be recovered by connecting to any number of nodes as long as the total amount of data downloaded is at least B. Similarly, regeneration of a failed node is possible if the new node connects to the network using links whose individual capacity is bounded above by beta(max) and whose sum capacity equals or exceeds a predetermined parameter gamma. In this flexible setting, we obtain the cut-set lower bound on the repair bandwidth along with a constructive proof for the existence of codes meeting this bound for all values of the parameters. An explicit code construction is provided which is optimal in certain parameter regimes.

Training-Symbol Embedded, High-Rate Complex Orthogonal Designs for Relay Networks

Distributed Space-Time Block Codes (DSTBCs) from Complex Orthogonal Designs (CODs) (both square and non-square CODs other than the Alamouti design) are known to lose their single-symbol ML decodable (SSD) property when used in two-hop wireless relay networks using the amplify and forward protocol. For such a network, a new class of high rate, training-symbol embedded (TSE) SSD DSTBCs are proposed from TSE-CODs. The constructed codes include the training symbols within the structure of the code which is shown to be the key point to obtain high rate along with the SSD property. TSE-CODs are shown to offer full-diversity for arbitrary complex constellations. Non-square TSE-CODs are shown to provide better rates (in symbols per channel use) compared to the known SSD DSTBCs for relay networks when the number of relays is less than 10. Importantly, the proposed DSTBCs do not contain zeros in their codewords and as a result, antennas of the relay nodes do not undergo a sequence of switch on and off transitions within every codeword use. Hence, the proposed DSTBCs eliminate the antenna switching problem.

Cooperative OFDM with Amplify-and-Forward Relaying with Timing Offset

In this paper, we investigate cooperative OFDM communications using amplify-and-forward (AF) protocol at the relays, in the presence of imperfect timing synchronization. In most studies on cooperative communications, perfect time synchronization among cooperating nodes is assumed. In practice, however, due to imperfect time synchronization, orthogonality among the subcarriers of the different nodes' signals at the destination receiver can be lost, causing inter-symbol interference (ISI). In this paper, we derive analytical expressions for the average SINR at the DFT output at the destination as a function of timing offset in cooperative OFDM with AF protocol, and illustrate the SINR degradation as a function of the timing offset. We also present an interference canceling (IC) receiver to mitigate the effects of ISI when there is timing offset. We show that the proposed IC receiver achieves improved BER performance even when timing offsets are large.

An Efficient Simulated Annealing With a Valid Solution Mechanism For TDMA Brodcast Scheduling problem

This paper presents an efficient Simulated Annealing with valid solution mechanism for finding an optimum conflict-free transmission schedule for a broadcast radio network. This is known as a Broadcast Scheduling Problem (BSP) and shown as an NP-complete problem, in earlier studies. Because of this NP-complete nature, earlier studies used genetic algorithms, mean field annealing, neural networks, factor graph and sum product algorithm, and sequential vertex coloring algorithm to obtain the solution. In our study, a valid solution mechanism is included in simulated annealing. Because of this inclusion, we are able to achieve better results even for networks with 100 nodes and 300 links. The results obtained using our methodology is compared with all the other earlier solution methods.

Multicode MIMO for High Data Rate Mobile Ad-hoc Networks

In a mobile ad-hoc network scenario, where communication nodes are mounted on moving platforms (like jeeps, trucks, tanks, etc.), use of V-BLAST requires that the number of receive antennas in a given node must be greater than or equal to the sum of the number of transmit antennas of all its neighbor nodes. This limits the achievable spatial multiplexing gain (data rate) for a given node. In such a scenario, we propose to achieve high data rates per node through multicode direct sequence spread spectrum techniques in conjunction with V-BLAST. In the considered multicode V-BLAST system, the receiver experiences code domain interference (CDI) in frequency selective fading, in addition to space domain interference (SDI) experienced in conventional V-BLAST systems. We propose two interference cancelling receivers that employ a linear parallel interference cancellation approach to handle the CDI, followed by conventional V-BLAST detector to handle the SDI, and then evaluate their bit error rates.

Design of logical topologies for wavelength-routed optical networks

his paper studies the problem of designing a logical topology over a wavelength-routed all-optical network (AON) physical topology, The physical topology consists of the nodes and fiber links in the network, On an AON physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics, The set of lightpaths along with the nodes constitutes the logical topology, For a given network physical topology and traffic pattern (relative traffic distribution among the source-destination pairs), our objective is to design the logical topology and the routing algorithm on that topology so as to minimize the network congestion while constraining the average delay seen by a source-destination pair and the amount of processing required at the nodes (degree of the logical topology), We will see that ignoring the delay constraints can result in fairly convoluted logical topologies with very long delays, On the other hand, in all our examples, imposing it results in a minimal increase in congestion, While the number of wavelengths required to imbed the resulting logical topology on the physical all optical topology is also a constraint in general, we find that in many cases of interest this number can be quite small, We formulate the combined logical topology design and routing problem described above (ignoring the constraint on the number of available wavelengths) as a mixed integer linear programming problem which we then solve for a number of cases of a six-node network, Since this programming problem is computationally intractable for larger networks, we split it into two subproblems: logical topology design, which is computationally hard and will probably require heuristic algorithms, and routing, which can be solved by a linear program, We then compare the performance of several heuristic topology design algorithms (that do take wavelength assignment constraints into account) against that of randomly generated topologies, as well as lower bounds derived in the paper.

Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics